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Proyecciones (Antofagasta)

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OUDGHIRI, Mourad  and  SOUILAH, Khalid. Non-linear maps preserving singular algebraic operators. Proyecciones (Antofagasta) [online]. 2016, vol.35, n.3, pp.301-316. ISSN 0716-0917.

Let B(H) be the algebra of all bounded linear operators on an infinite-dimensional Hilbert space H. We prove that if Φ is a surjective map on B(H) such that Φ(I) = I + Φ(0) and for every pair T, S ∈ B(H), the operator T - S is singular algebraic if and only if Φ(T) - Φ(S) is singular algebraic, then Φ is either of the form Φ(T) = ATA-1 + Φ(0) or the form Φ(T) = AT*A-1 + Φ(0) where A : H → H is an invertible bounded linear, or conjugate linear, operator.

Keywords : Non-linear preserver problems; Algebraic operators..

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